Propagation invariant beams, also known as “non-diffracting beams”, propagate indefinitely without changing their transverse intensity distribution. These optical fields are the well known plane waves, the Bessel beams [1]}, the Mathieu beams [2]} and the Weber beams [3]}. These invariant beams correspond to the solutions of the Helmholtz wave equation in Cartesian, circular cylindrical, parabolic cylindrical, and elliptical cylindrical coordinates, respectively. These non-diffracting beams have a large quantity of applications in fundamental and applied science in areas such as quantum mechanics [4]}, [5]}, [6]}, [7]}, acousto-optics [8]}, non-linear optics [9]}, optical tweezers [10]}, fluid dynamics [11]}, and optical communications [12]}, among others.
